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Title: On Two Nonintegrable Cases of the Generalized Henon-Heiles System

Abstract

The generalized Henon-Heiles system with an additional nonpolynomial term is considered. In two nonintegrable cases, new two-parameter solutions have been obtained in terms of elliptic functions. These solutions generalize the known one-parameter solutions. The singularity analysis shows that it is possible that three-parameter single-valued solutions exist in these two nonintegrable cases. The knowledge of the Laurent series solutions simplifies searches for the elliptic solutions and allows them to be automatized.

Authors:
 [1];  [2]
  1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119992 (Russian Federation)
  2. Central Astronomical Observatory at Pulkovo, St. Petersburg, 196140 (Russian Federation)
Publication Date:
OSTI Identifier:
20692915
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Atomic Nuclei; Journal Volume: 68; Journal Issue: 11; Other Information: Translated from Yadernaya Fizika, ISSN 0044-0027, 68, 2008-2016 (No. 11, 2005); DOI: 10.1134/1.2131124; (c) 2005 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA); TN:
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; FUNCTIONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS; SINGULARITY

Citation Formats

Vernov, S.Yu., and Timoshkova, E.I. On Two Nonintegrable Cases of the Generalized Henon-Heiles System. United States: N. p., 2005. Web. doi:10.1134/1.2131124.
Vernov, S.Yu., & Timoshkova, E.I. On Two Nonintegrable Cases of the Generalized Henon-Heiles System. United States. doi:10.1134/1.2131124.
Vernov, S.Yu., and Timoshkova, E.I. Tue . "On Two Nonintegrable Cases of the Generalized Henon-Heiles System". United States. doi:10.1134/1.2131124.
@article{osti_20692915,
title = {On Two Nonintegrable Cases of the Generalized Henon-Heiles System},
author = {Vernov, S.Yu. and Timoshkova, E.I.},
abstractNote = {The generalized Henon-Heiles system with an additional nonpolynomial term is considered. In two nonintegrable cases, new two-parameter solutions have been obtained in terms of elliptic functions. These solutions generalize the known one-parameter solutions. The singularity analysis shows that it is possible that three-parameter single-valued solutions exist in these two nonintegrable cases. The knowledge of the Laurent series solutions simplifies searches for the elliptic solutions and allows them to be automatized.},
doi = {10.1134/1.2131124},
journal = {Physics of Atomic Nuclei},
number = 11,
volume = 68,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}